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Earthworks Volume Computation AlgorithmCASLE Jamaica Regional and International Conference 10/10/12
H.A. Nandalal, Trinidad & Tobago Land Surveyor - www.survplan.com - [email protected]
A Robust Algorithmfor Earthworks
Volume Computations
Hakeeb A. Nandalal, BSc.Trinidad & Tobago Land Surveyor
http://[email protected]
Earthworks Volume Computation AlgorithmCASLE Jamaica Regional and International Conference 10/10/12
H.A. Nandalal, Trinidad & Tobago Land Surveyor - www.survplan.com - [email protected]
OVERVIEW:
Objectives Requirements Methodology The Algorithm
Earthworks Volume Computation AlgorithmCASLE Jamaica Regional and International Conference 10/10/12
H.A. Nandalal, Trinidad & Tobago Land Surveyor - www.survplan.com - [email protected]
OBJECTIVES
To obtain the Volume between Two Surfaces,Surface1 and Surface2
If Surface1 is 100% Above Surface2,this will be a “Cut” Volume Only
If Surface1 is 100% Below Surface2,this will be a “Fill” Volume Only
If Surface1 Intersects Surface2,there will be both a “Cut” Volume and a “Fill” Volume
Earthworks Volume Computation AlgorithmCASLE Jamaica Regional and International Conference 10/10/12
H.A. Nandalal, Trinidad & Tobago Land Surveyor - www.survplan.com - [email protected]
Surface1
Surface2
Surface1 Above Surface2: Cut Volume Only
Earthworks Volume Computation AlgorithmCASLE Jamaica Regional and International Conference 10/10/12
H.A. Nandalal, Trinidad & Tobago Land Surveyor - www.survplan.com - [email protected]
Surface1
Surface2
Surface1 Below Surface2: Fill Volume Only
Earthworks Volume Computation AlgorithmCASLE Jamaica Regional and International Conference 10/10/12
H.A. Nandalal, Trinidad & Tobago Land Surveyor - www.survplan.com - [email protected]
Surface1
Surface2
Surface1 Intersects Surface2: Cut & Fill Volumes
Surface1
Earthworks Volume Computation AlgorithmCASLE Jamaica Regional and International Conference 10/10/12
H.A. Nandalal, Trinidad & Tobago Land Surveyor - www.survplan.com - [email protected]
REQUIREMENTS
3D Data for Surface1 (Pre-Survey)
3D Data for Surface2 (Post-Survey)
A Method for Making Terrain Modelsfrom the 3D Data
An Algorithm for Comparing theTerrain Models to Derive
Cut & Fill Volumes
Earthworks Volume Computation AlgorithmCASLE Jamaica Regional and International Conference 10/10/12
H.A. Nandalal, Trinidad & Tobago Land Surveyor - www.survplan.com - [email protected]
OBTAINING THE 3D DATAMEASUREMENT METHODS:
1. Spot Heights with Total Stations/GPS
2. Ground-Based LIDAR*
3. Aerial Survey: Photography/LIDAR
*LIDAR : Light Detection and Ranging
Earthworks Volume Computation AlgorithmCASLE Jamaica Regional and International Conference 10/10/12
H.A. Nandalal, Trinidad & Tobago Land Surveyor - www.survplan.com - [email protected]
OBTAINING THE 3D DATA
Total Stations/GPS
Ground-Based LIDAR
Aerial Survey
GateWing X100
Earthworks Volume Computation AlgorithmCASLE Jamaica Regional and International Conference 10/10/12
H.A. Nandalal, Trinidad & Tobago Land Surveyor - www.survplan.com - [email protected]
Surface1 XYZ Data Surface2 XYZ Data
Earthworks Volume Computation AlgorithmCASLE Jamaica Regional and International Conference 10/10/12
H.A. Nandalal, Trinidad & Tobago Land Surveyor - www.survplan.com - [email protected]
Surface1 3D Points Plotted (Plan View)
Earthworks Volume Computation AlgorithmCASLE Jamaica Regional and International Conference 10/10/12
H.A. Nandalal, Trinidad & Tobago Land Surveyor - www.survplan.com - [email protected]
Surface1 3D Points Plotted (Side View)
20m
0m
Earthworks Volume Computation AlgorithmCASLE Jamaica Regional and International Conference 10/10/12
H.A. Nandalal, Trinidad & Tobago Land Surveyor - www.survplan.com - [email protected]
A METHOD FOR MAKING TERRAIN MODELSFROM THE 3D DATA
Delaunay Triangulation
In Mathematics and Computational Geometry,a Delaunay Triangulation for a Set of Pointsin a Plane, is a Triangulation such thatno other point in the Set is Inside the Circumcircleof a given Triangle.
The method is named after Boris Delaunayfor his work on this topic from 1934.
Earthworks Volume Computation AlgorithmCASLE Jamaica Regional and International Conference 10/10/12
H.A. Nandalal, Trinidad & Tobago Land Surveyor - www.survplan.com - [email protected]
Delaunay Triangulation of Surface1
This is a 2D Operation using only the X,YValues of the 3D Points
Earthworks Volume Computation AlgorithmCASLE Jamaica Regional and International Conference 10/10/12
H.A. Nandalal, Trinidad & Tobago Land Surveyor - www.survplan.com - [email protected]
Satisfying the Delaunay Triangulation Condition
Circumcircle
Earthworks Volume Computation AlgorithmCASLE Jamaica Regional and International Conference 10/10/12
H.A. Nandalal, Trinidad & Tobago Land Surveyor - www.survplan.com - [email protected]
The Triangulation AlgorithmDescribed in Pseudo-Code:
subroutine triangulateinput : vertex listoutput : triangle list initialize the triangle list determine the supertriangle add supertriangle vertices to the end of the vertex list add the supertriangle to the triangle list for each sample point in the vertex list initialize the edge buffer for each triangle currently in the triangle list calculate the triangle circumcircle center and radius if the point lies in the triangle circumcircle then add the three triangle edges to the edge buffer remove the triangle from the triangle list endif endfor delete all doubly specified edges from the edge buffer this leaves the edges of the enclosing polygon only add to the triangle list all triangles formed between the point and the edges of the enclosing polygon endfor remove any triangles from the triangle list that use the supertriangle vertices remove the supertriangle vertices from the vertex listend
Source: http://paulbourke.net/papers/triangulate
Earthworks Volume Computation AlgorithmCASLE Jamaica Regional and International Conference 10/10/12
H.A. Nandalal, Trinidad & Tobago Land Surveyor - www.survplan.com - [email protected]
OBTAINING VOLUMESFROM TERRAIN MODELS:
1. Between a Model and a Datum Plane
2. Between Two Models
Earthworks Volume Computation AlgorithmCASLE Jamaica Regional and International Conference 10/10/12
H.A. Nandalal, Trinidad & Tobago Land Surveyor - www.survplan.com - [email protected]
Volume Computation between a 3D Triangle and a Plane
Triangle Above Plane
Earthworks Volume Computation AlgorithmCASLE Jamaica Regional and International Conference 10/10/12
H.A. Nandalal, Trinidad & Tobago Land Surveyor - www.survplan.com - [email protected]
Volume Computation between a 3D Triangle and a Plane
Triangle Below Plane
Earthworks Volume Computation AlgorithmCASLE Jamaica Regional and International Conference 10/10/12
H.A. Nandalal, Trinidad & Tobago Land Surveyor - www.survplan.com - [email protected]
Volume Computation between a 3D Triangle and a Plane
Triangle Intersecting Plane
Earthworks Volume Computation AlgorithmCASLE Jamaica Regional and International Conference 10/10/12
H.A. Nandalal, Trinidad & Tobago Land Surveyor - www.survplan.com - [email protected]
Apply the Simple Computation toAll the 3D Triangles in the Model
Above
Below
Intersecting
Note: Slide #21
Datum Plane
Earthworks Volume Computation AlgorithmCASLE Jamaica Regional and International Conference 10/10/12
H.A. Nandalal, Trinidad & Tobago Land Surveyor - www.survplan.com - [email protected]
Surface1
Surface2
Volume between Two Models
Earthworks Volume Computation AlgorithmCASLE Jamaica Regional and International Conference 10/10/12
H.A. Nandalal, Trinidad & Tobago Land Surveyor - www.survplan.com - [email protected]
Plan View of Two Overlapping Models
Earthworks Volume Computation AlgorithmCASLE Jamaica Regional and International Conference 10/10/12
H.A. Nandalal, Trinidad & Tobago Land Surveyor - www.survplan.com - [email protected]
A Detailed View of the Overlap
Surface1
Surface2
Overlapping Shapes Can be Triangles, Quadrilaterals, Pentagons & Hexagons
Earthworks Volume Computation AlgorithmCASLE Jamaica Regional and International Conference 10/10/12
H.A. Nandalal, Trinidad & Tobago Land Surveyor - www.survplan.com - [email protected]
Typical Ways Two Triangles Can Overlap
All Overlap Shapes Can be Subdivided into Triangles
Earthworks Volume Computation AlgorithmCASLE Jamaica Regional and International Conference 10/10/12
H.A. Nandalal, Trinidad & Tobago Land Surveyor - www.survplan.com - [email protected]
THE COMPOSITE METHOD FOR OBTAINING THEVOLUME BETWEEN TWO SURFACES:
Identify the Overlapping Areas
Deconstruct the Complex Shapes (Quadrilaterals,Pentagons & Hexagons) into Triangles
Create a “Height Difference”or Isopach Triangulated Surface
Use the Simple Computation for Obtaining theCut/Fill Volumes between the Isopach Surface
and the Zero Plane
Earthworks Volume Computation AlgorithmCASLE Jamaica Regional and International Conference 10/10/12
H.A. Nandalal, Trinidad & Tobago Land Surveyor - www.survplan.com - [email protected]
Obtaining Z-Values of the Isopach Triangle
Vertically Non-Intersecting Planes
Earthworks Volume Computation AlgorithmCASLE Jamaica Regional and International Conference 10/10/12
H.A. Nandalal, Trinidad & Tobago Land Surveyor - www.survplan.com - [email protected]
When Planes Collide
Vertically Intersecting Planes
Earthworks Volume Computation AlgorithmCASLE Jamaica Regional and International Conference 10/10/12
H.A. Nandalal, Trinidad & Tobago Land Surveyor - www.survplan.com - [email protected]
The Two Surfaces The Isopach Surface
Earthworks Volume Computation AlgorithmCASLE Jamaica Regional and International Conference 10/10/12
H.A. Nandalal, Trinidad & Tobago Land Surveyor - www.survplan.com - [email protected]
Apply the Simple Computation toAll the 3D Triangles in the Model
Above
Below
Intersecting
Zero Plane
(Recall Slide #21)
The IsopachSurface
Earthworks Volume Computation AlgorithmCASLE Jamaica Regional and International Conference 10/10/12
H.A. Nandalal, Trinidad & Tobago Land Surveyor - www.survplan.com - [email protected]
Surface-To-Surface Volume Report
Surface1 Area = 10130.0 sq. mSurface2 Area = 10729.7 sq. mOverlapping Area = 10029.4 sq. mUnaffected Area = 0.0 sq. m
Area of Cut = 4879.8 sq. mArea of Fill = 5149.6 sq. mModified Area = 10029.4 sq. m
Max Z = 33.5 mMin Z = 14.2 mZ Range = 19.3 m
Cut Volume = 22198.39 Cubic MetresFill Volume = 17509.36 Cubic Metres
VOLUME REPORT USING THE COMPOSITE METHOD ON THETWO SURFACES USED IN THIS PRESENTATION(Windows Application Written in C by H. Nandalal)
Earthworks Volume Computation AlgorithmCASLE Jamaica Regional and International Conference 10/10/12
H.A. Nandalal, Trinidad & Tobago Land Surveyor - www.survplan.com - [email protected]
SURFACE TO SURFACE VOLUME REPORT
Trimble5475 Kellenburger RoadDayton, Ohio 45424-1099, USA1-937-233-8921
Project: C:\Temp\tm.proReport Generated: Friday, October 05, 2012 11:34:07 PM--------------------------------------------------------------------------------Where the second surface is above the first the volume is reported as fill.Where the second surface is below the first the volume is reported asexcavation.--------------------------------------------------------------------------------
Shrinkage/swell factors: Excavation 1.0000 Fill 1.0000
First Surface Number Second Surface NumberLayer Name of Points Layer Name of Points--------------------------- ----------- ------------------------- ----------SURFACE-1 121 SURFACE-2 121
Excavation Volume (Cu. m.) Fill Volume (Cu. m.)-------------------------------- ---------------------------- 22,198.39 17,509.36
Net Difference: 4,689.04 Cu. m. Waste
VOLUME REPORT USING THE COMPOSITE METHOD ON THETWO SURFACES USED IN THIS PRESENTATION
(Application: TerraModel)
Earthworks Volume Computation AlgorithmCASLE Jamaica Regional and International Conference 10/10/12
H.A. Nandalal, Trinidad & Tobago Land Surveyor - www.survplan.com - [email protected]
I would like to thank:
The Aubrey Barker Fund,Dr. Charisse Griffith-Charles
&CASLE Atlantic Region
for allowing me the opportunity topresent this paper.